German Patent Application No. DE 10 116 218 describes a valve actuator, in which one stem end of the gas exchange valve is connected to a positioning piston of the valve actuator via at least two shell-shaped wedge pieces which enclose the stem end and are axially supported by the positioning piston, the radially outer peripheral surface of the wedge pieces having a conical shape and being enclosed by a conical clamping sleeve. The conical clamping sleeve has a radially inner peripheral surface, whose shape is complementary to the conical angle of the wedge pieces and which is axially clamped against the wedge pieces by a threaded connection formed on the wedge pieces. Due to the conical angle and thread on the wedge pieces, these are relatively complex components, which are very costly to manufacture.